Murray, who came off the bench twice in last summer's victorious Lions series in Australia, is confident of providing Toulon with a stiff challenge.
However, he knows the French side's standing as reigning champions - and a star-studded line-up - will have many people doubting Munster's chances.
"It does annoy me when we hear the underdog tag," Murray told The Score. "And I know we'll have it against Toulon because of their international stars."
But Murray also knows the Munster side is packed with talent, including fellow Lions Simon Zebo and Paul O'Connell, and head coach Rob Penney is relishing an intense battle.
The Kiwi coach said: "We'll try and negate them as best we can and throw everything we have at them.
"I just hope the guys embrace it and enjoy it and aren't inhibited by anything physical or mental."